Problem: Simplify the following expression: $ x = \dfrac{p + 10}{4p - 6} + \dfrac{-9}{10} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{10}{10}$ $ \dfrac{p + 10}{4p - 6} \times \dfrac{10}{10} = \dfrac{10p + 100}{40p - 60} $ Multiply the second expression by $\dfrac{4p - 6}{4p - 6}$ $ \dfrac{-9}{10} \times \dfrac{4p - 6}{4p - 6} = \dfrac{-36p + 54}{40p - 60} $ Therefore $ x = \dfrac{10p + 100}{40p - 60} + \dfrac{-36p + 54}{40p - 60} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{10p + 100 - 36p + 54}{40p - 60} $ $x = \dfrac{-26p + 154}{40p - 60}$ Simplify the expression by dividing the numerator and denominator by 2: $x = \dfrac{-13p + 77}{20p - 30}$